# Suchergebnis: Katalogdaten im Herbstsemester 2016

Mathematik Master | ||||||

Wahlfächer Für das Master-Diplom in Angewandter Mathematik ist die folgende Zusatzbedingung (nicht in myStudies ersichtlich) zu beachten: Mindestens 15 KP der erforderlichen 28 KP aus Kern- und Wahlfächern müssen aus Bereichen der angewandten Mathematik und weiteren anwendungsorientierten Gebieten stammen. | ||||||

Wahlfächer aus Bereichen der reinen Mathematik | ||||||

Auswahl: Analysis | ||||||

Nummer | Titel | Typ | ECTS | Umfang | Dozierende | |
---|---|---|---|---|---|---|

401-4767-66L | Partial Differential Equations (Hyperbolic PDEs) | W | 7 KP | 4V | D. Christodoulou | |

Kurzbeschreibung | The course begins with characteristics, the definition of hyperbolicity, causal structure and the domain of dependence theorem. The course then focuses on nonlinear systems of equations in two independent variables, in particular the Euler equations of compressible fluids with plane symmetry and the Einstein equations of general relativity with spherical symmetry. | |||||

Lernziel | The objective is to introduce students in mathematics and physics to an area of mathematical analysis involving differential geometry which is of fundamental importance for the development of classical macroscopic continuum physics. | |||||

Inhalt | The course shall begin with the basic structure associated to hyperbolic partial differential equations, characteristic hypersurfaces and bicharacteristics, causal structure, and the domain of dependence theorem. The course shall then focus on nonlinear systems of equations in two independent variables. The first topic shall be the Euler equations of compressible fluids under plane symmetry where we shall study the formation of shocks, and second topic shall be the Einstein equations of general relativity under spherical symmetry where we shall study the formation of black holes and spacetime singularities. | |||||

Voraussetzungen / Besonderes | Basic real analysis and differential geometry. | |||||

401-4831-66L | Mathematical Themes in General Relativity I | W | 4 KP | 2V | A. Carlotto | |

Kurzbeschreibung | First part of a one-year course offering a rigorous introduction to general relativity, with special emphasis on aspects of current interest in mathematical research. Topics covered include: initial value formulation of the Einstein equations, causality theory and singularities, constructions of data sets by gluing or conformal methods, asymptotically flat spaces and positive mass theorems. | |||||

Lernziel | Acquisition of a solid and broad background in general relativity and mastery of the basic mathematical methods and ideas developed in such context and successfully exploited in the field of geometric analysis. | |||||

Inhalt | Lorentzian geometry; geometric review of special relativity; the Einstein equations and their basic classes of special solutions; the Einstein equations as an initial-value problem; causality theory and hyperbolicity; singularities and trapped domains; Penrose diagrams; asymptotically flat spaces: ADM invariants, positive mass theorems, Penrose inequalities, geometric properties. | |||||

Skript | Lecture notes written by the instructor will be provided to all enrolled students. | |||||

Voraussetzungen / Besonderes | The content of the basic courses of the first three years at ETH will be assumed. In particular, enrolled students are expected to be fluent both in Differential Geometry (at least at the level of Differentialgeometrie I, II) and Functional Analysis (at least at the level of Funktionalanalysis I, II). Some background on partial differential equations, mainly of elliptic and hyperbolic type, (say at the level of the monograph by L. C. Evans) would also be desirable. | |||||

401-4497-66L | Free Boundary Problems | W | 4 KP | 2V | A. Figalli | |

Kurzbeschreibung | ||||||

Lernziel | ||||||

401-4463-62L | Fourier Analysis in Function Space Theory | W | 6 KP | 3V | T. Rivière | |

Kurzbeschreibung | In the most important part of the course, we will present the notion of Singular Integrals and Calderón-Zygmund theory as well as its application to the analysis of linear elliptic operators. | |||||

Lernziel | ||||||

Inhalt | During the first lectures we will review the theory of tempered distributions and their Fourier transforms. We will go in particular through the notion of Fréchet spaces, Banach-Steinhaus for Fréchet spaces etc. We will then apply this theory to the Fourier characterization of Hilbert-Sobolev spaces. In the second part of the course we will study fundamental properties of the Hardy-Littlewood Maximal Function in relation with L^p spaces. We will then make a digression through the notion of Marcinkiewicz weak L^p spaces and Lorentz spaces. At this occasion we shall give in particular a proof of Aoki-Rolewicz theorem on the metrisability of quasi-normed spaces. We will introduce the preduals to the weak L^p spaces, the Lorentz L^{p',1} spaces as well as the general L^{p,q} spaces and show some applications of these dualities such as the improved Sobolev embeddings. In the third part of the course, the most important one, we will present the notion of Singular Integrals and Calderón-Zygmund theory as well as its application to the analysis of linear elliptic operators. This theory will naturally bring us, via the so called Littlewood-Paley decomposition, to the Fourier characterization of classical Hilbert and non Hilbert Function spaces which is one of the main goals of this course. If time permits we shall present the notion of Paraproduct, Paracompositions and the use of Littlewood-Paley decomposition for estimating products and general non-linearities. We also hope to cover fundamental notions from integrability by compensation theory such as Coifman-Rochberg-Weiss commutator estimates and some of its applications to the analysis of PDE. | |||||

Literatur | 1) Elias M. Stein, "Singular Integrals and Differentiability Properties of Functions" (PMS-30) Princeton University Press. 2) Javier Duoandikoetxea, "Fourier Analysis" AMS. 3) Loukas Grafakos, "Classical Fourier Analysis" GTM 249 Springer. 4) Loukas Grafakos, "Modern Fourier Analysis" GTM 250 Springer. | |||||

Voraussetzungen / Besonderes | Notions from ETH courses in Measure Theory, Functional Analysis I and II (Fundamental results in Banach and Hilbert Space theory, Fourier transform of L^2 Functions) | |||||

401-4475-66L | Partial Differential Equations and Semigroups of Bounded Linear Operators | W | 4 KP | 2G | A. Jentzen | |

Kurzbeschreibung | In this course we study the concept of a semigroup of bounded linear operators and we use this concept to investigate existence, uniqueness, and regularity properties of solutions of partial differential equations (PDEs) of the evolutionary type. | |||||

Lernziel | The aim of this course is to teach the students a decent knowledge (i) on semigroups of bounded linear operators, (ii) on solutions of partial differential equations (PDEs) of the evolutionary type, and (iii) on the analytic concepts used to formulate and study such semigroups and such PDEs. | |||||

Inhalt | The course includes content (i) on semigroups of bounded linear operators, (ii) on solutions of partial differential equations (PDEs) of the evolutionary type, and (iii) on the analytic concepts used to formulate and study such semigroups and such PDEs. Key example PDEs that are treated in this course are heat and wave equations. | |||||

Skript | Lecture Notes are available in the lecture homepage (please follow the link in the Learning materials section). | |||||

Literatur | 1. Amnon Pazy, Semigroups of linear operators and applications to partial differential equations. Springer-Verlag, New York (1983). 2. Klaus-Jochen Engel and Rainer Nagel, One-parameter semigroups for linear evolution equations. Springer-Verlag, New York (2000). | |||||

Voraussetzungen / Besonderes | Mandatory prerequisites: Functional analysis Start of lectures: Friday, September 23, 2016 For more details, please follow the link in the Learning materials section. | |||||

401-3303-00L | Ausgewählte Themen der Funktionentheorie | W | 6 KP | 3V | H. Knörrer | |

Kurzbeschreibung | Hypergeometrische Funktionen, Randwerte holomorpher Funktionen, Nevanlinna Theorie und andere spezielle Themen | |||||

Lernziel | Fortgeschrittene Methoden der Funktionentheorie | |||||

Literatur | R. Remmert: Funktionentheorie II. Springer Verlag E.Titchmarsh: The Theory of Functions. Oxford University Press C.Caratheodory: Funktionentheorie. Birkhaeuser E.Hille: Analytic Function Theory. AMS Chelsea Publishing A.Gogolin:Komplexe Integration. Springer | |||||

Voraussetzungen / Besonderes | Funktionentheorie | |||||

Auswahl: Weitere Gebiete | ||||||

Nummer | Titel | Typ | ECTS | Umfang | Dozierende | |

401-3502-66L | Reading Course DIE BELEGUNG ERFOLGT DURCH DAS STUDIENSEKRETARIAT. Bitte schicken Sie ein E-Mail an das Studiensekretariat D-MATH <studiensekretariat@math.ethz.ch> mit folgenden Angaben: 1) welchen Reading Course (60, 90, 120 Arbeitsstunden entsprechend 2, 3, 4 ECTS-Kreditpunkten) Sie belegen möchten; 2) in welchem Semester; 3) für welchen Studiengang; 4) Ihr Name und Vorname; 5) Ihre Studierenden-Nummer; 6) der Name und Vorname des Betreuers/der Betreuerin des Reading Courses. | W | 2 KP | 4A | Professor/innen | |

Kurzbeschreibung | In diesem Reading Course wird auf Eigeninitiative und auf individuelle Vereinbarung mit einem Dozenten/einer Dozentin hin ein Stoff durch eigenständiges Literaturstudium erarbeitet. | |||||

Lernziel | ||||||

401-3503-66L | Reading Course DIE BELEGUNG ERFOLGT DURCH DAS STUDIENSEKRETARIAT. Bitte schicken Sie ein E-Mail an das Studiensekretariat D-MATH <studiensekretariat@math.ethz.ch> mit folgenden Angaben: 1) welchen Reading Course (60, 90, 120 Arbeitsstunden entsprechend 2, 3, 4 ECTS-Kreditpunkten) Sie belegen möchten; 2) in welchem Semester; 3) für welchen Studiengang; 4) Ihr Name und Vorname; 5) Ihre Studierenden-Nummer; 6) der Name und Vorname des Betreuers/der Betreuerin des Reading Courses. | W | 3 KP | 6A | Professor/innen | |

Kurzbeschreibung | In diesem Reading Course wird auf Eigeninitiative und auf individuelle Vereinbarung mit einem Dozenten/einer Dozentin hin ein Stoff durch eigenständiges Literaturstudium erarbeitet. | |||||

Lernziel | ||||||

401-3504-66L | Reading Course DIE BELEGUNG ERFOLGT DURCH DAS STUDIENSEKRETARIAT. Bitte schicken Sie ein E-Mail an das Studiensekretariat D-MATH <studiensekretariat@math.ethz.ch> mit folgenden Angaben: 1) welchen Reading Course (60, 90, 120 Arbeitsstunden entsprechend 2, 3, 4 ECTS-Kreditpunkten) Sie belegen möchten; 2) in welchem Semester; 3) für welchen Studiengang; 4) Ihr Name und Vorname; 5) Ihre Studierenden-Nummer; 6) der Name und Vorname des Betreuers/der Betreuerin des Reading Courses. | W | 4 KP | 9A | Professor/innen | |

Kurzbeschreibung | In diesem Reading Course wird auf Eigeninitiative und auf individuelle Vereinbarung mit einem Dozenten/einer Dozentin hin ein Stoff durch eigenständiges Literaturstudium erarbeitet. | |||||

Lernziel | ||||||

Wahlfächer aus Bereichen der angewandten Mathematik ... vollständiger Titel: Wahlfächer aus Bereichen der angewandten Mathematik und weiteren anwendungsorientierten Gebieten | ||||||

Auswahl: Numerische Mathematik | ||||||

Nummer | Titel | Typ | ECTS | Umfang | Dozierende | |

401-4657-00L | Numerical Analysis of Stochastic Ordinary Differential Equations Alternative course title: "Computational Methods for Quantitative Finance: Monte Carlo and Sampling Methods" | W | 6 KP | 3V + 1U | A. Jentzen | |

Kurzbeschreibung | Course on numerical approximations of stochastic ordinary differential equations driven by Wiener processes. These equations have several applications, for example in financial option valuation. This course also contains an introduction to random number generation and Monte Carlo methods for random variables. | |||||

Lernziel | The aim of this course is to enable the students to carry out simulations and their mathematical convergence analysis for stochastic models originating from applications such as mathematical finance. For this the course teaches a decent knowledge of the different numerical methods, their underlying ideas, convergence properties and implementation issues. | |||||

Inhalt | Generation of random numbers Monte Carlo methods for the numerical integration of random variables Stochastic processes and Brownian motion Stochastic ordinary differential equations (SODEs) Numerical approximations of SODEs Multilevel Monte Carlo methods for SODEs Applications to computational finance: Option valuation | |||||

Skript | Lecture Notes are available in the lecture homepage (please follow the link in the Learning materials section). | |||||

Literatur | P. Glassermann: Monte Carlo Methods in Financial Engineering. Springer-Verlag, New York, 2004. P. E. Kloeden and E. Platen: Numerical Solution of Stochastic Differential Equations. Springer-Verlag, Berlin, 1992. | |||||

Voraussetzungen / Besonderes | Prerequisites: Mandatory: Probability and measure theory, basic numerical analysis and basics of MATLAB programming. a) mandatory courses: Elementary Probability, Probability Theory I. b) recommended courses: Stochastic Processes. Start of lectures: Wednesday, September 21, 2016 For more details, please follow the link in the Learning materials section. | |||||

401-4785-00L | Mathematical and Computational Methods in Photonics | W | 8 KP | 4G | H. Ammari | |

Kurzbeschreibung | The aim of this course is to review new and fundamental mathematical tools, computational approaches, and inversion and optimal design methods used to address challenging problems in nanophotonics. The emphasis will be on analyzing plasmon resonant nanoparticles, super-focusing & super-resolution of electromagnetic waves, photonic crystals, electromagnetic cloaking, metamaterials, and metasurfaces | |||||

Lernziel | The field of photonics encompasses the fundamental science of light propagation and interactions in complex structures, and its technological applications. The recent advances in nanoscience present great challenges for the applied and computational mathematics community. In nanophotonics, the aim is to control, manipulate, reshape, guide, and focus electromagnetic waves at nanometer length scales, beyond the resolution limit. In particular, one wants to break the resolution limit by reducing the focal spot and confine light to length scales that are significantly smaller than half the wavelength. Interactions between the field of photonics and mathematics has led to the emergence of a multitude of new and unique solutions in which today's conventional technologies are approaching their limits in terms of speed, capacity and accuracy. Light can be used for detection and measurement in a fast, sensitive and accurate manner, and thus photonics possesses a unique potential to revolutionize healthcare. Light-based technologies can be used effectively for the very early detection of diseases, with non-invasive imaging techniques or point-of-care applications. They are also instrumental in the analysis of processes at the molecular level, giving a greater understanding of the origin of diseases, and hence allowing prevention along with new treatments. Photonic technologies also play a major role in addressing the needs of our ageing society: from pace-makers to synthetic bones, and from endoscopes to the micro-cameras used in in-vivo processes. Furthermore, photonics are also used in advanced lighting technology, and in improving energy efficiency and quality. By using photonic media to control waves across a wide band of wavelengths, we have an unprecedented ability to fabricate new materials with specific microstructures. The main objective in this course is to report on the use of sophisticated mathematics in diffractive optics, plasmonics, super-resolution, photonic crystals, and metamaterials for electromagnetic invisibility and cloaking. The course merges highly nontrivial multi-mathematics in order to make a breakthrough in the field of mathematical modelling, imaging, and optimal design of optical nanodevices and nanostructures capable of light enhancement, and of the focusing and guiding of light at a subwavelength scale. We demonstrate the power of layer potential techniques in solving challenging problems in photonics, when they are combined with asymptotic analysis and the elegant theory of Gohberg and Sigal on meromorphic operator-valued functions. In this course we shall consider both analytical and computational matters in photonics. The issues we consider lead to the investigation of fundamental problems in various branches of mathematics. These include asymptotic analysis, spectral analysis, mathematical imaging, optimal design, stochastic modelling, and analysis of wave propagation phenomena. On the other hand, deriving mathematical foundations, and new and efficient computational frameworks and tools in photonics, requires a deep understanding of the different scales in the wave propagation problem, an accurate mathematical modelling of the nanodevices, and fine analysis of complex wave propagation phenomena. An emphasis is put on mathematically analyzing plasmon resonant nanoparticles, diffractive optics, photonic crystals, super-resolution, and metamaterials. | |||||

Auswahl: Wahrscheinlichkeitstheorie, Statistik | ||||||

Nummer | Titel | Typ | ECTS | Umfang | Dozierende | |

401-4604-66L | Topics in Probability Theory | W | 4 KP | 2V | W. Werner | |

Kurzbeschreibung | The goal of this course is to give a sample of some basic results and features to illustrate various areas of probability theory. | |||||

Lernziel | The goal of this course is to give a sample of some basic results and features to illustrate various areas of probability theory. | |||||

401-3604-66L | Special Topics in Probability | W | 4 KP | 2V | P. Nolin | |

Kurzbeschreibung | The goal of this course is to present recent developments in Percolation Theory | |||||

Lernziel | The goal of this course is to present recent developments in Percolation Theory | |||||

Inhalt | Independent percolation is obtained by deleting randomly (and independently) the edges of a lattice, each with a given probability p between 0 and 1. One is then interested in the connectivity properties of the random subgraph so-obtained. It is arguably the simplest model from statistical mechanics that displays a phase transition, a drastic change of behavior as the parameter p varies. We will first present classical tools and properties of percolation theory: in particular correlation inequalities, exponential decay of connection probabilities, and uniqueness of the infinite connected component. We will then discuss recent developments: for example percolation on Cayley graphs, and continuum limits in two dimensions. | |||||

Literatur | B. Bollobas, O. Riordan: Percolation, CUP 2006 G. Grimmett: Percolation 2ed, Springer 1999 | |||||

Voraussetzungen / Besonderes | Prerequisites: 401-2604-00L Probability and Statistics (mandatory) 401-3601-00L Probability Theory (recommended) | |||||

401-4611-66L | Rough Path Theory and Regularity Structures | W | 6 KP | 3V | J. Teichmann, D. Prömel | |

Kurzbeschreibung | The course provides an introduction to the theory of controlled rough paths with focus on stochastic differential equations. In parallel, Martin Hairer's new theory of regularity structures is introduced taking controlled rough paths as guiding examples. In particular, the course demonstrates how to use the theory of regularity structures to solve singular stochastic PDEs. | |||||

Lernziel | The main goal is to develop simultaneously the basic concepts of rough path theory and Hairer's regularity structures. | |||||

Literatur | - Peter Friz and Martin Hairer, A Course on Rough Paths: With an Introduction to Regularity Structures, Springer, 2014. - Martin Hairer, Introduction to regularity structures, Braz. J. Probab. Stat. 29 (2015), no. 2, 175-210. - Peter Friz and Nicolas Victoir, Multidimensional stochastic processes as rough paths. Theory and applications, Cambridge University Press, 2010. - Martin Hairer, A theory of regularity structures, Inventiones mathematicae (2014), 1-236. - Ajay Chandra and Hendrik Weber, Stochastic PDEs, Regularity Structures, and Inter- acting Particle Systems, Preprint arXiv:1508.03616. | |||||

Voraussetzungen / Besonderes | Requirements: Brownian Motion and Stochastic Calculus | |||||

401-3627-00L | High-Dimensional StatisticsFindet dieses Semester nicht statt. | W | 4 KP | 2V | P. L. Bühlmann | |

Kurzbeschreibung | "High-Dimensional Statistics" deals with modern methods and theory for statistical inference when the number of unknown parameters is of much larger order than sample size. Statistical estimation and algorithms for complex models and aspects of multiple testing will be discussed. | |||||

Lernziel | Knowledge of methods and basic theory for high-dimensional statistical inference | |||||

Inhalt | Lasso and Group Lasso for high-dimensional linear and generalized linear models; Additive models and many smooth univariate functions; Non-convex loss functions and l1-regularization; Stability selection, multiple testing and construction of p-values; Undirected graphical modeling | |||||

Literatur | Peter Bühlmann and Sara van de Geer (2011). Statistics for High-Dimensional Data: Methods, Theory and Applications. Springer Verlag. ISBN 978-3-642-20191-2. | |||||

Voraussetzungen / Besonderes | Knowledge of basic concepts in probability theory, and intermediate knowledge of statistics (e.g. a course in linear models or computational statistics). | |||||

401-4623-00L | Time Series Analysis | W | 6 KP | 3G | N. Meinshausen | |

Kurzbeschreibung | Statistical analysis and modeling of observations in temporal order, which exhibit dependence. Stationarity, trend estimation, seasonal decomposition, autocorrelations, spectral and wavelet analysis, ARIMA-, GARCH- and state space models. Implementations in the software R. | |||||

Lernziel | Understanding of the basic models and techniques used in time series analysis and their implementation in the statistical software R. | |||||

Inhalt | This course deals with modeling and analysis of variables which change randomly in time. Their essential feature is the dependence between successive observations. Applications occur in geophysics, engineering, economics and finance. Topics covered: Stationarity, trend estimation, seasonal decomposition, autocorrelations, spectral and wavelet analysis, ARIMA-, GARCH- and state space models. The models and techniques are illustrated using the statistical software R. | |||||

Skript | Not available | |||||

Literatur | A list of references will be distributed during the course. | |||||

Voraussetzungen / Besonderes | Basic knowledge in probability and statistics | |||||

401-3612-00L | Stochastic Simulation | W | 5 KP | 3G | F. Sigrist | |

Kurzbeschreibung | This course provides an introduction to statistical Monte Carlo methods. This includes applications of simulations in various fields (Bayesian statistics, statistical mechanics, operations research, financial mathematics), algorithms for the generation of random variables (accept-reject, importance sampling), estimating the precision, variance reduction, introduction to Markov chain Monte Carlo. | |||||

Lernziel | Stochastic simulation (also called Monte Carlo method) is the experimental analysis of a stochastic model by implementing it on a computer. Probabilities and expected values can be approximated by averaging simulated values, and the central limit theorem gives an estimate of the error of this approximation. The course shows examples of the many applications of stochastic simulation and explains different algorithms used for simulation. These algorithms are illustrated with the statistical software R. | |||||

Inhalt | Examples of simulations in different fields (computer science, statistics, statistical mechanics, operations research, financial mathematics). Generation of uniform random variables. Generation of random variables with arbitrary distributions (quantile transform, accept-reject, importance sampling), simulation of Gaussian processes and diffusions. The precision of simulations, methods for variance reduction. Introduction to Markov chains and Markov chain Monte Carlo (Metropolis-Hastings, Gibbs sampler, Hamiltonian Monte Carlo, reversible jump MCMC). | |||||

Skript | A script will be available in English. | |||||

Literatur | P. Glasserman, Monte Carlo Methods in Financial Engineering. Springer 2004. B. D. Ripley. Stochastic Simulation. Wiley, 1987. Ch. Robert, G. Casella. Monte Carlo Statistical Methods. Springer 2004 (2nd edition). | |||||

Voraussetzungen / Besonderes | Familiarity with basic concepts of probability theory (random variables, joint and conditional distributions, laws of large numbers and central limit theorem) will be assumed. | |||||

401-3611-00L | Advanced Topics in Computational StatisticsFindet dieses Semester nicht statt. | W | 4 KP | 2V | M. H. Maathuis | |

Kurzbeschreibung | This lecture covers selected advanced topics in computational statistics, including various classification methods, the EM algorithm, clustering, handling missing data, and graphical modelling. | |||||

Lernziel | Students learn the theoretical foundations of the selected methods, as well as practical skills to apply these methods and to interpret their outcomes. | |||||

Inhalt | The course is roughly divided in three parts: (1) Supervised learning via (variations of) nearest neighbor methods, (2) the EM algorithm and clustering, (3) handling missing data and graphical models. | |||||

Skript | Lecture notes. | |||||

Voraussetzungen / Besonderes | We assume a solid background in mathematics, an introductory lecture in probability and statistics, and at least one more advanced course in statistics. | |||||

401-0649-00L | Applied Statistical Regression | W | 5 KP | 2V + 1U | M. Dettling | |

Kurzbeschreibung | This course offers a practically oriented introduction into regression modeling methods. The basic concepts and some mathematical background are included, with the emphasis lying in learning "good practice" that can be applied in every student's own projects and daily work life. A special focus will be laid in the use of the statistical software package R for regression analysis. | |||||

Lernziel | The students acquire advanced practical skills in linear regression analysis and are also familiar with its extensions to generalized linear modeling. | |||||

Inhalt | The course starts with the basics of linear modeling, and then proceeds to parameter estimation, tests, confidence intervals, residual analysis, model choice, and prediction. More rarely touched but practically relevant topics that will be covered include variable transformations, multicollinearity problems and model interpretation, as well as general modeling strategies. The last third of the course is dedicated to an introduction to generalized linear models: this includes the generalized additive model, logistic regression for binary response variables, binomial regression for grouped data and poisson regression for count data. | |||||

Skript | A script will be available. | |||||

Literatur | Faraway (2005): Linear Models with R Faraway (2006): Extending the Linear Model with R Draper & Smith (1998): Applied Regression Analysis Fox (2008): Applied Regression Analysis and GLMs Montgomery et al. (2006): Introduction to Linear Regression Analysis | |||||

Voraussetzungen / Besonderes | The exercises, but also the classes will be based on procedures from the freely available, open-source statistical software package R, for which an introduction will be held. In the Mathematics Bachelor and Master programmes, the two course units 401-0649-00L "Applied Statistical Regression" and 401-3622-00L "Regression" are mutually exclusive. Registration for the examination of one of these two course units is only allowed if you have not registered for the examination of the other course unit. | |||||

401-0625-01L | Applied Analysis of Variance and Experimental Design | W | 5 KP | 2V + 1U | L. Meier | |

Kurzbeschreibung | Principles of experimental design. One-way analysis of variance. Multi-factor experiments and analysis of variance. Block designs. Latin square designs. Split-plot and strip-plot designs. Random effects and mixed effects models. Full factorials and fractional designs. | |||||

Lernziel | Participants will be able to plan and analyze efficient experiments in the fields of natural sciences. They will gain practical experience by using the software R. | |||||

Inhalt | Principles of experimental design. One-way analysis of variance. Multi-factor experiments and analysis of variance. Block designs. Latin square designs. Split-plot and strip-plot designs. Random effects and mixed effects models. Full factorials and fractional designs. | |||||

Literatur | G. Oehlert: A First Course in Design and Analysis of Experiments, W.H. Freeman and Company, New York, 2000. | |||||

Voraussetzungen / Besonderes | The exercises, but also the classes will be based on procedures from the freely available, open-source statistical software R, for which an introduction will be held. |

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